Abstract
A mathematic model of Green function is build for two dimension free water surface. The analytic expression of Green function is obtained by introducing a parameter of complex number. The intrinsic properties of Green function are discussed for the special parameter values. The real and imaginary parts of H function are shown in the paper.
Highlights
Researches on ship’s hydrodynamics force need to work out the added mass
The near field two dimensional added mass is generally calculated by boundary integral method, in which the Green function is often used as the kernel function
As long as the number of terms in series M is known, we can calculate the values of H(Y) and the Green function based on the proposed formula before
Summary
Researches on ship’s hydrodynamics force need to work out the added mass. The near field two dimensional added mass is generally calculated by boundary integral method, in which the Green function is often used as the kernel function. Since the Green function can be represented by improper integral with several singularities and an infinite integrating range, problems of calculation errors and large mount of calculation naturally arise. It causes scholars’ interests to study on the Green function with free surface for years. In 2010, French scholar Ricardo [4] published his research results of the Green function, which pointed out that if using infinite series or integral to represent the two-dimensional frequency domain Green function with free surface, it has an ambiguous theory discourse, a huge mount of computation and some inconvenience in practical. Based on the work of Ricardo [4], this paper theoretically discusses the near-field two-dimensional Green function with free surface about its inherent properties using complex function theories
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